Article

# The PHEMU15 catalog and astrometric results of the Jupiter’s Galilean satellite mutual occultation and eclipse observations made in 2014-2015.★†

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## Abstract

During the 2014-2015 mutual events season, the Institut de Mécanique Céleste et de Calcul des Éphémérides (IMCCE), Paris France, and the Sternberg Astronomical Institute (SAI), Moscow Russia, led an international observation campaign to record ground-based photometric observations of Galilean moon mutual occultations and eclipses. We focused on processing the complete photometric observations database to compute new accurate astrometric positions. We used our method to derive astrometric positions from the lightcurves of the events. We developed an accurate photometric model of mutual occultations and eclipses, while correcting for the satellite albedos, Hapke’s light scattering law, the phase effect and the limb darkening. We processed 609 lightcurves and we compared the observed positions of the satellites with the theoretical positions from IMCCE NOE-5-2010-GAL satellite ephemerides and INPOP13c planetary ephemeris. The standard deviation after fitting the light curve in equatorial positions is ±24 mas, or 75 km at Jupiter. The rms (O-C) in equatorial positions is ±50 mas, or 150 km at Jupiter.

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... The photometry of these events offers a reliable source of very precise relative positions between two satellites. They often achieve uncertainties bellow 5 mas (∼ 15 km) (Emelyanov, 2009;Dias-Oliveira et al., 2013;Arlot et al., 2014a;Saquet et al., 2018). These relative positions can constrain the orbital studies of these moons and give us hints about their structure and formation processes (Lainey et al., 2004b,a, ⋆ Based in part on observations made at the Laboratório Nacional de Astrofísica (LNA), Itajubá-MG, Brazil. ...
... However, this approach demands previous knowledge about the satellite surface (albedo maps) that can change with time or even for different effective wavelengths, it is important to highlight that these maps are not know for the wavelength of our observations ( 0 = 889 nm). The same applies to the Hapke scattering law (Hapke, 1981;Hapke and Wells, 1981;Hapke, 1984Hapke, , 1986Hapke, , 2002Hapke, , 2008Hapke, , 2012 used by Emelyanov (2009), Arlot et al. (2014a) and Saquet et al. (2018), which requires unknown parameters in the wavelength band of our observations. ...
... Also, two other stations in the USA observed this event, one in Arnold (AAC) and another in Scottsdale (SCO). These observations were made in the context of the international mu- tual phenomena campaign PHEMU15, (Saquet et al., 2018;Emel'yanov, 2017). Both light curves are available at the NSDB. ...
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Progress in astrometry and orbital modelling of planetary moons in the last decade enabled better determinations of their orbits. These studies need accurate positions spread over extended periods. We present the results of the 2014-2015 Brazilian campaign for 40 mutual events from 47 observed light curves by the Galilean satellites plus one eclipse of Amalthea by Ganymede. We also reanalysed and updated results for 25 mutual events observed in the 2009 campaign. All telescopes were equipped with narrow-band filters centred at 889 nm with a width of 15 nm to eliminate the scattered light from Jupiter. The albedos' ratio was determined using images before and after each event. We simulated images of moons, umbra, and penumbra in the sky plane, and integrated their fluxes to compute albedos, simulate light curves and fit them to the observed ones using a chi-square fitting procedure. For that, we used the complete version of the Oren-Nayer reflectance model. The relative satellite positions mean uncertainty was 11.2 mas ($\sim$35 km) and 10.1 mas ($\sim$31 km) for the 2014-2015 and 2009 campaigns respectively. The simulated and observed \textsc{ascii} light curve files are freely available in electronic form at the \textit{Natural Satellites DataBase} (NSDB). The 40/25 mutual events from our 2014-2015/2009 campaigns represent a significant contribution of 17%/15% in comparison with the PHEMU campaigns lead by the IMCCE. Besides that, our result for the eclipse of Amalthea is only the 4$^{th}$ such measurement ever published after the three ones observed by the 2014-2015 international PHEMU campaign. Our results are suitable for new orbital/ephemeris determinations for the Galilean moons and Amalthea.
... Mutual events can be observed on the Earth twice during one orbital period of planet, that is to say every six years for the Galilean satellites. Since 1973, the first observation (Aksnes & Franklin 1976), several observational campaigns of the mutual events between natural satellites had been performed, and the detailed history of all the past campaigns of mutual events between the natural satellites can be seen in Saquet et al. (2018) and its references. The most recent observation period of the mutual events between the Galilean satellites was during 2014-2015 (Vasundhara, Selvakumar & Anbazhagan 2017;Saquet et al. 2018). ...
... Since 1973, the first observation (Aksnes & Franklin 1976), several observational campaigns of the mutual events between natural satellites had been performed, and the detailed history of all the past campaigns of mutual events between the natural satellites can be seen in Saquet et al. (2018) and its references. The most recent observation period of the mutual events between the Galilean satellites was during 2014-2015 (Vasundhara, Selvakumar & Anbazhagan 2017;Saquet et al. 2018). ...
Article
Observation of mutual events has been confirmed to be a most effective and accurate ground-based method for obtaining accurate astrometric data by fitting the flux variation of involved satellites during the events, which is very invaluable for improving the orbital models of the natural satellites. The mutual events between the Galilean satellites occur every six years. During the observational campaign of 2014-2015, 21 mutual events between Galilean satellites were observed with the SARA 0.9 m and 0.6 m telescopes. The model proposed by Assafin et al. and Zhang et al. for mutual occultation and Zhang et al. for mutual eclipse were used to fit the light curves, taking the Lommel-Seeliger scattering law and the solar limb darkening into account. In this paper, the astrometric results of the Galilean satellites from the mutual events we observed will be shown, such as the impact parameter and its corresponding mid-time, and the velocity of occulting/eclipsing satellite relative to the occulted/eclipsed one. © 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society.
... A constant da/dt parameter (that can be converted into dn/dt) was fitted for Io, Europa and Ganymede. They considered all observations in Lainey et al. (2009) and added the mutual events campaign of 2009 and 2016 (Arlot et al., 2014;Saquet et al., 2018). ...
Article
Full-text available
... For the Galileans satellites, mutual phenomena may deliver relative positions with a precision better than 5 mas (Dias-Oliveira et al. 2013;Emelyanov 2009). More than 600 light curves were obtained in the last Mutual phenomena campaign between the Galilean moons, the PHEMU15, with an average precision of 24 mas (Saquet et al. 2018). ...
Article
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The technique of mutual approximations accurately gives the central instant at the maximum apparent approximation of two moving natural satellites in the sky plane. This can be used in ephemeris fitting to infer the relative positions between satellites with high precision. Only the mutual phenomena-occultations and eclipses-may achieve better results. However, mutual phenomena only occur every six years in the case of Jupiter. Mutual approximations do not have this restriction and can be observed at any time along the year as long as the satellites are visible. In this work, we present 104 central instants determined from the observations of 66 mutual approximations between the Galilean moons carried out at different sites in Brazil and France during the period 2016-2018. For 28 events we have at least two independent observations. All telescopes were equipped with a narrow-band filter centred at 889 nm with a width of 15 nm to eliminate the scattered light from Jupiter. The telescope apertures ranged between 25-120 cm. For comparison, the precision of the positions obtained with classical CCD astrometry is about 100 mas, for mutual phenomena it can achieve 10 mas or less and the average internal precision obtained with mutual approximations was 11.3 mas. This new kind of simple, yet accurate observations can significantly improve the orbits and ephemeris of Galilean satellites and thus be very useful for the planning of future space missions aiming at the Jovian system.
... The case of Galilean moons is a critical example because Jupiter's brightness in the Field of View (FoV) would quickly saturate the CCD, thus providing positions with uncertainties that range between 100 and 150 milliarcseconds (mas; Kiseleva et al. 2008). This scenario motivates the search for alternative methods for the astrometry of these satellites, such as the mutual phenomena events (Aksnes & Franklin 1976;Aksnes et al. 1984;Emelyanov 2009;Arlot et al. 2014;Saquet et al. 2018;Morgado et al. 2019c, and references therein), mutual approximations (Morgado et al. 2016(Morgado et al. , 2019a, radar astrometry (Brozović et al. 2020), and stellar occultations (Morgado et al. 2019b), among others. ...
Article
Full-text available
A stellar occultation occurs when a Solar System object passes in front of a star for an observer. This technique allows the sizes and shapes of the occulting body to be determined with kilometer precision. In addition, this technique constrains the occulting body’s positions, albedos, densities, and so on. In the context of the Galilean moons, these events can provide their best ground-based astrometry, with uncertainties in the order of 1 mas (∼3 km at Jupiter’s distance during opposition). We organized campaigns and successfully observed a stellar occultation by Io (JI) in 2021, one by Ganymede (JIII) in 2020, and one by Europa (JII) in 2019, with stations in North and South America. We also re-analyzed two previously published events: one by Europa in 2016 and another by Ganymede in 2017. We then fit the known 3D shape of the occulting satellite and determine its center of figure. This resulted in astrometric positions with uncertainties in the milliarcsecond level. The positions obtained from these stellar occultations can be used together with dynamical models to ensure highly accurate orbits of the Galilean moons. These orbits can help when planning future space probes aiming at the Jovian system, such as JUICE by ESA and Europa Clipper by NASA. They also allow more efficient planning of flyby maneuvers.
... The case of Galilean moons is a critical example since Jupiter's brightness in the Field of View (FoV) would quickly saturate the CCD, thus providing positions with uncertainties that range between 100 and 150 milliarcseconds (mas) (Kiseleva et al. 2008). This scenario motivates the search for alternative methods for the astrometry of these satellites, for example, the mutual phenomena events (Aksnes & Franklin 1976;Aksnes et al. 1984;Emelyanov 2009;Arlot et al. 2014;Saquet et al. 2018;Morgado et al. 2019c, and references therein), mutual approximations (Morgado et al. 2016(Morgado et al. , 2019a, radar astrometry (Brozović et al. 2020), stellar occultations (Morgado et al. 2019b), among others. ...
Preprint
Full-text available
A stellar occultation occurs when a Solar System object passes in front of a star for an observer. This technique allows the determination of sizes and shapes of the occulting body with kilometer precision. Also, this technique constrains the occulting body's positions, albedos, densities, etc. In the context of the Galilean moons, these events can provide their best ground-based astrometry, with uncertainties in the order of 1 mas ($\sim$ 3 km at Jupiter's distance during opposition). We organized campaigns and successfully observed a stellar occultation by Io (JI) in 2021, one by Ganymede (JIII) in 2020, and one by Europa (JII) in 2019, with stations in North and South America. Also, we re-analyzed two previously published events, one by Europa in 2016 and another by Ganymede in 2017. Then, we fit the known 3D shape of the occulting satellite and determine its center of figure. That resulted in astrometric positions with uncertainties in the milliarcsecond level. The positions obtained from these stellar occultations can be used together with dynamical models to ensure highly accurate orbits of the Galilean moons. These orbits can help plan future space probes aiming at the Jovian system, such as JUICE by ESA and Europa Clipper by NASA, and allow more efficient planning of flyby maneuvers.
... By studying a (spatially resolved) occultation of Io by Europa, de Kleer et al. (2017) mapped the Loki Patera (Patera is a type of an irregular crater) region to a precision of about 2 kilometers. In addition to observations of occultations in the near infrared, several groups have been observing mutual occultations in the optical for decades with the purpose of inferring the optical albedo of Io and improving ephemeris precision for Galilean satellites (Arlot et al. 1974;Saquet et al. 2018;Morgado et al. 2016, and references therein). Understanding the detailed albedo distribution is crucial to constraining the ephemeris of Io to a very high precision. ...
Preprint
Jupiter's moon Io is the most volcanically active body in the Solar System with hundreds of active volcanoes varying in intensity on different timescales. Io has been observed during occultations by other Galilean moons and Jupiter since the 1980s, using high-cadence near infrared photometry. These observations encode a wealth of information about the volcanic features on its surface. We built a generative model for the observed occultations using the code starry which enables fast, analytic, and differentiable computation of occultation light curves in emitted and reflected light. Our probabilistic Bayesian model is able to recover known hotspots on the surface of Io using only two light curves and without any assumptions on the locations, shapes or the number of spots. The methods we have developed are also directly applicable to the problem of mapping the surfaces of stars and exoplanets.
... Saquet et al. (2018) observed mutual events from 2014 to 2015 and reported a measurement uncertainty of ∼24 mas. The rms of the residuals in the plane-of-sky coordinates was 65.5 mas with respect to JPL's JUP310 and planetary ephemeris DE430(Folkner et al. 2014).Saquet et al. measurements are orthogonal with respect to our radar ranging measurements, and their relatively large residuals are not at odds with the small radar residuals in ...
... Before 2021, several observational campaigns were completed during previous occurrences (Arlot et al. 1992(Arlot et al. , 1997(Arlot et al. , 2006(Arlot et al. , 2014Saquet 2018 ). Table 1 presents the results derived for each campaign until the present one. ...
Article
2021 was the year of Jupiter’s equinox, that is the Sun and the Earth passed through the equatorial plane of the planet and therefore the orbital planes of its main satellites. This occurrence made it possible to observe mutual occultations and eclipses between the satellites. Our former experience shows that observations of such events provide accurate astrometric data that can be used to obtain new information on the dynamics of the Galilean satellites. The observations are a series of photometric measurements of a satellite which are carried out through the organization of a world wide campaign of observations thus maximizing the number and the quality of the data obtained. This work focuses on processing the photometric observations of the mutual occultations and eclipses of the Galilean satellites of Jupiter made during the international campaign in 2021. The final goal is to derive new accurate astrometric data. We used an accurate photometric model of mutual events in conjunction with the accuracy of observation. We obtained and processed the 84 light curves obtained during the campaign. As compared with the current best ephemerides, the rms of ’O-C’ residuals are equal to 49 and 48 mas in right ascension and declination, respectively.
... A constant da/dt parameter (that can be converted into dn/dt) was fitted for Io, Europa and Ganymede. They considered all observations in Lainey et al. (2009) and added the mutual events campaign of 2009 and 2016 (Arlot et al., 2014;Saquet et al., 2018). ...
Article
Article
There is wide interest in the results of studies of the dynamics of satellites of planets. Such data are needed to determine the physical properties of celestial bodies, and they may be able to provide information about the origins and evolution of the solar system. The general approach to studying the dynamics of satellites involves developing models for the motion and ephemerides based on observational data. Ephemerides are required to prepare and launch space missions to other planets and help discover new celestial bodies. High-precision astrometric coordinates of the principal satellites of Jupiter, Saturn, and Uranus are derived from photometric observations of occultations and eclipses of these satellites. To this end, worldwide observing campaigns have been organized. Enhancement in the precision of ephemerides can be obtained not only by increasing the accuracy of observations, but also by expanding the time interval covered by the observations. Many new, distant satellites of the major planets were discovered in the early 21st century. However, observations of these satellites are scarce and were obtained over short time intervals; as a result, some of these satellites were lost. To date, 179 natural satellites are known. This paper is based on a presentation made at the conference “Modern Astrometry 2017,” dedicated to the memory of K.V. Kuimov (Sternberg Astronomical Institute, Moscow State University, October 23–25, 2017).
Article
Astrometry of Solar system objects needs to perform observations regularly since the motions are fast and the dynamical models need sample of data on long intervals of time. The goal of this paper is to show that some phenomena occurring during the equinox on the giant planets are worth to be observed. Past experience has shown the interest of such observations which should be continued in the future due to their relevant contribution to improve the dynamical models. Using the best ephemerides of the natural planetary satellites, we calculate the next phenomena to occur in order to prepare the future observational campaigns. We provide in this paper the tables of the dates of the next phenomena as their observational conditions which depends on the opposition and the declination of the planet. Past observations provided particularly accurate data, better than all the other ground based observations and we encourage observations in the next future especially for planetary systems for which no space mission is planned.
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Context. Bright stellar positions are now known with an uncertainty below 1 mas thanks to Gaia DR2. Between 2019-2020, the Galactic plane will be the background of Jupiter. The dense stellar background will lead to an increase in the number of occultations, while the Gaia DR2 catalogue will reduce the prediction uncertainties for the shadow path. Aims. We observed a stellar occultation by the Galilean moon Europa (J2) and propose a campaign for observing stellar occultations for all Galilean moons. Methods. During a predicted period of time, we measured the light flux of the occulted star and the object to determine the time when the flux dropped with respect to one or more reference stars, and the time that it rose again for each observational station. The chords obtained from these observations allowed us to determine apparent sizes, oblatness, and positions with kilometre accuracy. Results. We present results obtained from the first stellar occultation by the Galilean moon Europa observed on 2017 March 31. The apparent fitted ellipse presents an equivalent radius of 1561.2 � 3.6 km and oblatenesses 0.0010 � 0.0028. A very precise Europa position was determined with an uncertainty of 0.8 mas. We also present prospects for a campaign to observe the future events that will occur between 2019 and 2021 for all Galilean moons. Conclusions. Stellar occultation is a suitable technique for obtaining physical parameters and highly accurate positions of bright satellites close to their primary. A number of successful events can render the 3D shapes of the Galilean moons with high accuracy. We encourage the observational community (amateurs included) to observe the future predicted events.
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Photometric observation of mutual events between planetary satellites can be used to obtain their high accurate astrometric data. The mutual events between the Galilean satellites occur every six years. During 2014–15, 12 mutual events between the Galilean satellites were observed using 1.0 m telescope in Kunming and the fourth of Burst Optical Observer and Transient Exploring System (hereafter Bootes-4) 0.6 m telescope at Lijiang station of Yunnan Observatories, Chinese Academy of Sciences, and the astrometric results of such mutual events will be given in this paper.
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Mutual events (MEs) are eclipses and occultations among planetary natural satellites. Most of the time, eclipses and occultations occur separately. However, the same satellite pair will exhibit an eclipse and an occultation quasi-simultaneously under particular orbital configurations. This kind of rare event is termed as a quasi-simultaneous mutual event (“QSME”). During the 2021 campaign of mutual events of jovian satellites, we observed a QSME between Europa and Ganymede. The present study aims to describe and study the event in detail. We observed the QSME with a CCD camera attached to a 30-cm telescope at the Hong Kong Space Museum Sai Kung iObservatory. We obtained the combined flux of Europa and Ganymede from aperture photometry. A geometric model was developed to explain the light curve observed. Our results are compared with theoretical predictions (“O-C”). We found that our simple geometric model can explain the QSME fairly accurately, and the QSME light curve is a superposition of the light curves of an eclipse and an occultation. Notably, the observed flux drops are within 2.6% of the theoretical predictions. The size of the event central time O-C’s ranges from −14.4 to 43.2 s. Both O-C’s of flux drop and timing are comparable to other studies adopting more complicated models. Given the event rarity, model simplicity and accuracy, we encourage more observations and analysis on QSMEs to improve Solar System ephemerides.
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Progress in astrometry and orbital modelling of planetary moons in the last decade enabled better determinations of their orbits. These studies need accurate positions spread over extended periods. We present the results of the 2014–2015 Brazilian campaign for 40 mutual events from 47 observed light curves by the Galilean satellites plus one eclipse of Amalthea by Ganymede. We also reanalysed and updated results for 25 mutual events observed in the 2009 campaign. All telescopes were equipped with narrow-band filters centred at 889 nm with a width of 15 nm to eliminate the scattered light from Jupiter. The albedos’ ratio was determined using images before and after each event. We simulated images of moons, umbra, and penumbra in the sky plane, and integrated their fluxes to compute albedos, simulate light curves and fit them to the observed ones using a chi-square fitting procedure. For that, we used the complete version of the Oren-Nayer reflectance model. The relative satellite positions mean uncertainty was 11.2 mas (~35 km) and 10.1 mas (~31 km) for the 2014–2015 and 2009 campaigns respectively. The simulated and observed ascii light curve files are freely available in electronic form at the Natural Satellites DataBase (NSDB). The 40/25 mutual events from our 2014–2015/2009 campaigns represent a significant contribution of 17%/15% in comparison with the PHEMU campaigns lead by the IMCCE. Besides that, our result for the eclipse of Amalthea is only the 4th such measurement ever published after the three ones observed by the 2014–2015 international PHEMU campaign. Our results are suitable for new orbital/ephemeris determinations for the Galilean moons and Amalthea.
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We present the results of observations of the Galilean moons of Jupiter carried out at the Normal Astrograph of the Pulkovo Observatory in 2018. We obtained 452 positions of the Galilean moons of Jupiter in the Gaia DR1 catalog system (ICRF, J2000.0) and 671 differential coordinates of the satellites relative to each other. The obtained mean errors in the satellites’ normal positions on the right ascension and declination, which demonstrate the intrinsic convergence of the observational results, are εα = 0.003′′ and εδ = 0.003′′, respectively, for the entire observational period. The errors of one difference are σα = 0.070′′, and σδ = 0.067′′, respectively. The equatorial coordinates of the moons were compared to eight motion theories of planets and satellites. On average, the (O–C) residuals in the both coordinates relative to the motion theories are 0.014′′. The best agreement with observations is achieved by combination of all four motion theories of satellites with the planetary theory EPM2017, which yields average (O–C) residuals of approximately 0.01′′ for each of them. The new results were compared to those of the 2016−2017 observational season. As in the past, peculiarities in the behavior of the (O–C) residuals for Io and Ganymede have been noticed.
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New versions of the ephemerides for the Galilean satellites of Jupiter (Io, Europa, Ganymede, and Callisto) constructed by numerically integrating the equations of motion of the satellites are presented. The satellite motionmodel takes into account the non-sphericity of Jupiter, the mutual perturbations of the satellites, and the perturbations from the Sun and major planets. The initial satellite motion parameters have been improved based on all the available series of ground-based optical observations spanning the interval 1891-2017, spacecraft observations, and radar observations. As a result, the coefficients of the expansion of the satellite coordinates and velocities in terms of Chebyshev polynomials in the interval 1891- 2025 have been obtained. The root-mean-square errors of the observations and the graphs of comparison of the constructed ephemerides both with the observations and with Lainey's numerical ephemerides are presented. The constructed ephemerides are publicly accessible.
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A valuable source of astrometric data for studying the dynamics of natural satellites of planets are photometric observations of satellites during their mutual occultations and eclipses. Worldwide photometric campaigns are organized in order to observe as many events as possible. For the events that took place in 1985 and 1990–1992, the results of photometric observations of the Galilean satellites of Jupiter were published as timings of minimum light flux and values of flux drop expressed in magnitudes. These data were not suitable to refine the theory of motion of these satellites. This paper presents the results of a new reduction of the satellite astrometric coordinate differences deduced from the photometric observations of the Galilean satellites of Jupiter during their mutual occultations and eclipses in 1985 and 1990–1992. An original method of reduction that has been earlier developed by the authors was applied. This provides a significant portion of new high quality data for the general database of existing observations. The internal accuracy of obtained astrometric results is 16 mas for the observations made in 1985 and 28 mas for those made in 1990–1992. The data are included into the Natural Satellite Data Base and are available at http://nsdb.imcce.fr/obspos/bjupogae.htm.
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With hundreds of active volcanoes varying in intensity on different timescales, Jupiter’s moon Io is the most volcanically active body in the solar system. Io has been observed from Earth using high-cadence near-infrared photometry during occultations by Jupiter and other Galilean moons since the 1980s. These observations encode a wealth of information about the volcanic features on its surface. We built a generative model for the observed occultation light curves using the code starry , which enables fast, analytic, and differentiable computation of occultation light curves in emitted and reflected light. Using this model, we are able to recover surface thermal emission maps of Io containing known volcanic hot spots without having to make assumptions about the locations, shapes, or number of hot spots. Our model is also directly applicable to the problem of mapping the surfaces of stars and exoplanets.
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We derive efficient, closed-form, differentiable, and numerically stable solutions for the flux measured from a spherical planet or moon seen in reflected light, either in or out of occultation. Our expressions apply to the computation of scattered light phase curves of exoplanets, secondary eclipse light) curves in the optical, or future measurements of planet–moon and planet–planet occultations, as well as to photometry of solar system bodies. We derive our solutions for Lambertian bodies illuminated by a point source, but extend them to model illumination sources of finite angular size and rough surfaces with phase-dependent scattering. Our algorithm is implemented in Python within the open-source starry mapping framework and is designed with efficient gradient-based inference in mind. The algorithm is ∼4–5 orders of magnitude faster than direct numerical evaluation methods and ∼10 orders of magnitude more precise. We show how the techniques developed here may one day lead to the construction of two-dimensional maps of terrestrial planet surfaces, potentially enabling the detection of continents and oceans on exoplanets in the habitable zone. ⁶ ⁶ https://github.com/rodluger/starrynight
• J E Arlot
Arlot J. E. et al., 1992, A&AS, 92, 151
• J E Arlot
Arlot J. E. et al., 1997, A&AS, 125, 399
• J.-E Arlot
Arlot J.-E. et al., 2006, A&A, 451, 733
• J.-E Arlot
Arlot J.-E. et al., 2009, A&A, 493, 1171
• J.-E Arlot
Arlot J.-E. et al., 2014, A&A, 572, A120
• D Dirkx
• V Lainey
• L I Gurvits
• P N A M Visser
Dirkx D., Lainey V., Gurvits L. I., Visser P. N. A. M., 2016, Planet. Space Sci., 134, 82
• N V Emelianov
Emelianov N. V., 2003, Sol. Sys. Res., 37, 314
• N V Emelyanov
• R Gilbert
Emelyanov N. V., Gilbert R., 2006, A&A, 453, 1141
• V Lainey
• L Duriez
• A Vienne
Lainey V., Duriez L., Vienne A., 2004a, A&A, 420, 1171
• V Lainey
• J E Arlot
• A Vienne
Lainey V., Arlot J. E., Vienne A., 2004b, A&A, 427, 371
• V Lainey
• V Dehant
• M Pätzold
Lainey V., Dehant V., Pätzold M., 2007, A&A, 465, 1075
• W D Pence
• L Chiappetti
• C G Page
• R A Shaw
• E Stobie
Pence W. D., Chiappetti L., Page C. G., Shaw R. A., Stobie E., 2010, A&A, 524, A42
• A Fienga
• H Manche
• M Gastineau
• A Verna
Fienga A., Manche H., Laskar J., Gastineau M., Verna A., 2014, in INPOP new release: INPOP13c. IMCCE, Observatoire de Paris, Paris Gaia Collaboration et al., 2016, A&A, 595, A2
• R Jacobson
Jacobson R., 2013, JUP 310 Release, available at: http://naif.jpl.nasa.gov/ pub/naif/JUNO/kernels/spk/jup310.bsp.lbl
• V Robert
• E Saquet
• F Colas
• J.-E Arlot
Robert V., Saquet E., Colas F., Arlot J.-E., 2017, MNRAS, 467, 694
Moscow State University -Sternberg astronomical institute
• M V Lomonosov
M. V. Lomonosov Moscow State University -Sternberg astronomical institute, 13 Universitetskij prospect, 119992 Moscow, Russia
France 74 SAF groupe Alsace, 8 rue des ormes, F-67450 Mundolsheim, France 75 Club Eclipse, 22 rue du Borrego -BAL149, F-75020 Paris, France 76 International Occultation Timing Association
Université Lille 1, Impasse de l'Observatoire, F-59000 Lille, France 74 SAF groupe Alsace, 8 rue des ormes, F-67450 Mundolsheim, France 75 Club Eclipse, 22 rue du Borrego -BAL149, F-75020 Paris, France 76 International Occultation Timing Association, European Section (IOTA-ES), Bahnhofstrasse 117, D-16359 Biesenthal, Germany 77 Pod Lipou 1532, Hořice, Czech Republic This paper has been typeset from a T E X/L A T E X file prepared by the author. MNRAS 474, 4730-4739 (2018)
• V Lainey
• J.-E Arlot
• Karatekinö
• T Van Hoolst
Lainey V., Arlot J.-E., KaratekinÖ., van Hoolst T., 2009, Nature, 459, 957
rue de l'Ardèche, F-31170 Tournefeuille, France 18 Observatório Nacional MCTI, rua Gal
• Société Astronomique De France
Société Astronomique de France, commission des observations planétaires, 2, rue de l'Ardèche, F-31170 Tournefeuille, France 18 Observatório Nacional MCTI, rua Gal. J. Cristino 77, Rio de Janeiro, RJ, 20921-400, Brazil 19 Club Eclipse, 1 rue des Peupliers, F-92190 Meudon, France 20 Naperville, near Chicago, IL 60540, USA 21 Observatoire de Dax, rue Pascal Lafitte, F-40100 Dax, France 22 International Occultation Timing Association (IOTA), PO Box 7152, Kent, WA 98042, USA